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Popular >

simplify e^{-x}(1+x)*e^x

Solution

simplify

e^{- x} (1 + x) \cdot e^{x}

Solution

x + 1

Solution steps

e^{- x} (1 + x) e^{x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- x} e^{x} = e^{- x + x}

= (1 + x) e^{- x + x}

Add similar elements:

- x + x = 0

= (1 + x) e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot (x + 1)

Multiply:

(1 + x) \cdot 1 = (1 + x)

= (1 + x)

Remove parentheses:

(a) = a

= 1 + x

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Frequently Asked Questions (FAQ)

What is e^{-x}(1+x)*e^x ?
The solution to e^{-x}(1+x)*e^x is x+1